This book examines four mathematical concepts which play a great role in many different areas of mathematics: symbolic sums, recurrence (difference) equations, generating functions, and asymptotic estimates.

The book treats four mathematical concepts which play a fundamental role in many different areas of mathematics: symbolic sums, recurrence (difference) equations, generating functions, and asymptotic estimates.

Their key features, in isolation or in combination, their mastery by paper and pencil or by computer programs, and their applications to problems in pure mathematics or to "real world problems" (e.g. the analysis of algorithms) are studied. The book is intended as an algorithmic supplement to the bestselling "Concrete Mathematics" by Graham, Knuth and Patashnik.

Concrete mathematics from a computer algebra perspective Informal style: as simple as possible, as complicated as necessary Includes notivating applications from combinatorics, computer science, number theory, special functions Includes supplementary material: sn.pub/extras

Autorentext

Manuel Kauers ist als Professor für Algebra an der Johannes Kepler Universität in Linz tätig. Er befasst sich vor allem mit Computeralgebra, einem Forschungsgebiet im Grenzbereich zwischen Mathematik und Informatik. Neben zwei Fachbüchern über Computeralgebra hat er gemeinsam mit Koautoren aus aller Welt mehr als hundert wissenschaftliche Artikel publiziert und wurde mehrfach für seine Arbeit ausgezeichnet.

Inhalt

1 Introduction.- 2 Formal Power Series.- 3 Polynomials.- 4 C-Finite Sequences.- 5 Hypergeometric Series.- 6 Algebraic Functions.- 7 Holonomic Sequences and Power Series.- Appendix.- References.- Index.